As a corollary, we can show that a weighted graph has a good cut if and only if its second weighted Laplacian eigenvalue \(\lambda _2\)  is small. The harder direction of Corollary REF  was also proved by Friedman and Tillich, who also studied graph Laplacians with general vertex and edge measures, in [1]}, which generalises [2]} and [3]} for the combinatorial and normalised Laplacians, respectively.
